Analisis dinamik model SVEIR pada penyebaran penyakit campak

Sitty Oriza Sativa Putri Ahaya (Jurusan Matematika, Universitas Negeri Gorontalo)
Emli Rahmi (Jurusan Matematika, Universitas Negeri Gorontalo)
Nurwan Nurwan (Jurusan Matematika, Universitas Negeri Gorontalo)

Jambura Journal of Biomathematics (JJBM)
Volume 1, Issue 2: December 2020

In this article, we analyze the dynamics of measles transmission model with vaccination via an SVEIR epidemic model. The total population is divided into five compartments, namely the Susceptible, Vaccinated, Exposed, Infected, and Recovered populations. Firstly, we determine the equilibrium points and their local asymptotically stability properties presented by the basic reproduction number R0. It is found that the disease free equilibrium point is locally asymptotically stable if satisfies R01 and the endemic equilibrium point is locally asymptotically stable when R01. We also show the existence of forward bifurcation driven by some parameters that influence the basic reproduction number R0 i.e., the infection rate α or proportion of vaccinated individuals θ. Lastly, some numerical simulations are performed to support our analytical results.